Self-oscillatory dynamics of the metabolic process in a cell

TL;DR

This paper models the self-oscillatory behavior of cellular metabolism using nonlinear dynamics, analyzing bifurcations, chaos, and self-organization phenomena through mathematical tools.

Contribution

It introduces a detailed mathematical model of cellular metabolic oscillations and explores their bifurcation scenarios and chaotic transitions.

Findings

Identification of bifurcation scenarios leading to chaos in metabolic dynamics

Construction of phase portraits and Poincaré maps of attractors

Demonstration of classical nonlinear tools applied to cellular metabolism

Abstract

In this work, a mathematical model of self-oscillatory dynamics of the metabolism in a cell is studied. The full phase-parametric characteristics of variations of the form of attractors depending on the dissipation of a kinetic membrane potential are calculated. The bifurcations and the scenarios of the transitions {\guillemotleft}order-chaos{\guillemotright}, {\guillemotleft}chaos-order{\guillemotright} and {\guillemotleft}order-order{\guillemotright} are found. We constructed the projections of the multidimensional phase portraits of attractors, Poincar\'e sections, and Poincar\'e maps. The process of self-organization of regular attractors through the formation torus was investigated. The total spectra of Lyapunov exponents and the divergences characterizing a structural stability of the determined attractors are calculated. The results obtained demonstrate the possibility of the application of classical tools of nonlinear dynamics to the study of the self-organization and the appearance of a chaos in the metabolic process in a cells.